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Properties

Label 720.6
Level 720
Weight 6
Dimension 28094
Nonzero newspaces 28
Sturm bound 165888
Trace bound 9

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Defining parameters

Level: \( N \) = \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 28 \)
Sturm bound: \(165888\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(720))\).

Total New Old
Modular forms 70016 28336 41680
Cusp forms 68224 28094 40130
Eisenstein series 1792 242 1550

Trace form

\( 28094 q - 12 q^{2} - 12 q^{3} + 32 q^{4} - 5 q^{5} - 48 q^{6} + 12 q^{7} - 504 q^{8} + 84 q^{9} + O(q^{10}) \) \( 28094 q - 12 q^{2} - 12 q^{3} + 32 q^{4} - 5 q^{5} - 48 q^{6} + 12 q^{7} - 504 q^{8} + 84 q^{9} + 380 q^{10} - 390 q^{11} - 16 q^{12} - 844 q^{13} + 696 q^{14} + 1659 q^{15} + 11464 q^{16} - 3642 q^{17} - 16056 q^{18} - 3068 q^{19} - 6296 q^{20} + 6014 q^{21} + 31368 q^{22} + 8692 q^{23} + 32304 q^{24} + 21247 q^{25} - 7736 q^{26} - 12360 q^{27} - 43512 q^{28} - 71442 q^{29} - 31204 q^{30} + 4038 q^{31} - 18472 q^{32} + 41190 q^{33} + 64808 q^{34} + 38184 q^{35} - 60712 q^{36} + 28082 q^{37} + 105672 q^{38} - 116346 q^{39} + 163444 q^{40} - 24566 q^{41} + 60864 q^{42} + 41612 q^{43} - 107056 q^{44} + 3757 q^{45} - 211528 q^{46} + 428916 q^{47} - 224760 q^{48} - 64596 q^{49} - 89348 q^{50} - 34388 q^{51} + 46760 q^{52} - 147910 q^{53} + 230632 q^{54} - 211910 q^{55} + 109008 q^{56} - 208016 q^{57} + 257312 q^{58} + 65918 q^{59} + 234348 q^{60} + 204410 q^{61} + 351672 q^{62} + 372534 q^{63} - 128176 q^{64} - 12571 q^{65} - 7488 q^{66} - 286956 q^{67} - 278736 q^{68} - 688250 q^{69} + 212516 q^{70} - 540972 q^{71} - 1113072 q^{72} + 532106 q^{73} - 741408 q^{74} + 265649 q^{75} - 1328 q^{76} + 514298 q^{77} + 92280 q^{78} - 96710 q^{79} + 256696 q^{80} + 789916 q^{81} - 384136 q^{82} + 682736 q^{83} + 2211920 q^{84} - 573708 q^{85} + 687152 q^{86} + 140478 q^{87} + 367848 q^{88} - 226396 q^{89} - 614616 q^{90} - 251096 q^{91} - 714392 q^{92} + 474314 q^{93} - 497880 q^{94} - 626000 q^{95} - 1214392 q^{96} + 289608 q^{97} - 1971284 q^{98} - 978702 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(720))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
720.6.a \(\chi_{720}(1, \cdot)\) 720.6.a.a 1 1
720.6.a.b 1
720.6.a.c 1
720.6.a.d 1
720.6.a.e 1
720.6.a.f 1
720.6.a.g 1
720.6.a.h 1
720.6.a.i 1
720.6.a.j 1
720.6.a.k 1
720.6.a.l 1
720.6.a.m 1
720.6.a.n 1
720.6.a.o 1
720.6.a.p 1
720.6.a.q 1
720.6.a.r 1
720.6.a.s 1
720.6.a.t 1
720.6.a.u 1
720.6.a.v 1
720.6.a.w 1
720.6.a.x 1
720.6.a.y 2
720.6.a.z 2
720.6.a.ba 2
720.6.a.bb 2
720.6.a.bc 2
720.6.a.bd 2
720.6.a.be 2
720.6.a.bf 2
720.6.a.bg 2
720.6.a.bh 2
720.6.a.bi 3
720.6.a.bj 3
720.6.b \(\chi_{720}(71, \cdot)\) None 0 1
720.6.d \(\chi_{720}(649, \cdot)\) None 0 1
720.6.f \(\chi_{720}(289, \cdot)\) 720.6.f.a 2 1
720.6.f.b 2
720.6.f.c 2
720.6.f.d 2
720.6.f.e 2
720.6.f.f 2
720.6.f.g 2
720.6.f.h 4
720.6.f.i 4
720.6.f.j 4
720.6.f.k 4
720.6.f.l 6
720.6.f.m 6
720.6.f.n 8
720.6.f.o 8
720.6.f.p 16
720.6.h \(\chi_{720}(431, \cdot)\) 720.6.h.a 16 1
720.6.h.b 24
720.6.k \(\chi_{720}(361, \cdot)\) None 0 1
720.6.m \(\chi_{720}(359, \cdot)\) None 0 1
720.6.o \(\chi_{720}(719, \cdot)\) 720.6.o.a 4 1
720.6.o.b 8
720.6.o.c 8
720.6.o.d 40
720.6.q \(\chi_{720}(241, \cdot)\) n/a 240 2
720.6.t \(\chi_{720}(181, \cdot)\) n/a 400 2
720.6.u \(\chi_{720}(179, \cdot)\) n/a 480 2
720.6.w \(\chi_{720}(17, \cdot)\) n/a 120 2
720.6.x \(\chi_{720}(127, \cdot)\) n/a 150 2
720.6.z \(\chi_{720}(163, \cdot)\) n/a 596 2
720.6.bc \(\chi_{720}(197, \cdot)\) n/a 480 2
720.6.bd \(\chi_{720}(307, \cdot)\) n/a 596 2
720.6.bg \(\chi_{720}(53, \cdot)\) n/a 480 2
720.6.bi \(\chi_{720}(343, \cdot)\) None 0 2
720.6.bj \(\chi_{720}(233, \cdot)\) None 0 2
720.6.bl \(\chi_{720}(251, \cdot)\) n/a 320 2
720.6.bm \(\chi_{720}(109, \cdot)\) n/a 596 2
720.6.br \(\chi_{720}(239, \cdot)\) n/a 360 2
720.6.bt \(\chi_{720}(119, \cdot)\) None 0 2
720.6.bv \(\chi_{720}(121, \cdot)\) None 0 2
720.6.bw \(\chi_{720}(191, \cdot)\) n/a 240 2
720.6.by \(\chi_{720}(49, \cdot)\) n/a 356 2
720.6.ca \(\chi_{720}(169, \cdot)\) None 0 2
720.6.cc \(\chi_{720}(311, \cdot)\) None 0 2
720.6.ce \(\chi_{720}(229, \cdot)\) n/a 2864 4
720.6.cf \(\chi_{720}(11, \cdot)\) n/a 1920 4
720.6.ci \(\chi_{720}(7, \cdot)\) None 0 4
720.6.cl \(\chi_{720}(137, \cdot)\) None 0 4
720.6.cm \(\chi_{720}(77, \cdot)\) n/a 2864 4
720.6.cp \(\chi_{720}(43, \cdot)\) n/a 2864 4
720.6.cq \(\chi_{720}(173, \cdot)\) n/a 2864 4
720.6.ct \(\chi_{720}(187, \cdot)\) n/a 2864 4
720.6.cu \(\chi_{720}(113, \cdot)\) n/a 712 4
720.6.cx \(\chi_{720}(223, \cdot)\) n/a 720 4
720.6.da \(\chi_{720}(59, \cdot)\) n/a 2864 4
720.6.db \(\chi_{720}(61, \cdot)\) n/a 1920 4

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(720))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(720)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 20}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 18}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 15}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(360))\)\(^{\oplus 2}\)